Fractal Quasi-Coulomb Crystals in Ion Trap with Cantor Dust Electrode Configuration

Abstract

We propose a new concept of fractal quasi-Coulomb crystals. We have shown that self-similar quasi-Coulomb crystals can be formed in surface electrodynamic traps with the Cantor Dust electrode configuration. Quasi-Coulomb crystal fractal dimension appears to depend on the electrode parameters. We have identified the conditions for transforming trivial quasi-Coulomb crystals into self-similar crystals and described the features of forming 25 Ca+ self-similar quasi-Coulomb crystals. The local potential well depth and width have been shown to take a discrete value dependent on the distance from the electrode surface. Ions inside the crystals studied possess varied translational secular frequencies. We believe that the extraordinary properties of self-similar quasi-Coulomb crystals may contribute to the new prospects within levitated optomechanics, quantum computing and simulation.

Keywords

• surface ion trap
• quasi-Coulomb crystals
• Minkowski dimension
• Cantor Dust
• optomechanics